This is a homework problem of mine. The professor said we can use any resource to help us solve and I cannot get up with anyone from class. Please help. I'm not looking for a direct answer, I really need someone to help me solve this step by step.
You own two liquor distribution sites in two different locations. You receive orders from two customers. Customer A needs 50 gallons. Customer B needs 70 gallons. Your East side store has 80 gallons. Your West side store has 45 gallons. Delivery cost per gallon are: from east store 0.50 for A, 0.60 for B and from your west store 0.40 for A and 0.55 for B.
How do you arrange your shipping to minimize your cost
P.s. Sorry, I corrected it The east store has 80 gallons not 45.
Hint: $$cost = \frac4{10}n_w + \frac12 n_e +\frac{55}{100}p_w +\frac6{10}p_e $$
$ $
$ $n_w$ is the number of gallons sent from the west store to A
$n_e$ is the number of gallons sent from the east store to A
$p_w$ is the number of gallons sent from the west store to B
$p_e$ is the number of gallons sent from the east store to B
$$ $$ observe that:$$ \frac4{10}\lt \frac12 \lt \frac{55}{100}\lt \frac6{10} $$
How can you "distribute" the number of gallons so that the cost is minimized?